What is the solution for (d^2y)/(dx^2)y+81y=0 ?

The solution for (d^2y)/(dx^2)y+81y=0 is y=-(81x^2)/2+c_{1}x+c_{2}

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(d^2y)/(dx^2)y+81y=0

\frac{d ^{2} y}{d x ^{2}} y + 81 y = 0

y = - \frac{81 x ^{2}}{2} + c_{1} x + c_{2}

Solution steps

\frac{d ^{2} y}{d x ^{2}} y + 81 y = 0

Substitute

\frac{d ^{2} y}{d x ^{2}}

with

y^{''} (x)

y^{^{''}} (x) y + 81 y = 0

Isolate

y^{''} (x) : y^{''} (x) = - 81

Solve

y^{''} (x) = - 81 : y^{'} (x) = - 81 x + c_{1}

Solve

y^{'} (x) = - 81 x + c_{1} : y = - \frac{81 x ^{2}}{2} + c_{1} x + c_{2}

y = - \frac{81 x ^{2}}{2} + c_{1} x + c_{2}

y^{^{'}} = k x

x \to \infty lim (4 x + 7)

\int (x + 2) (x^{2} + x - 1) d x

t \to 0 lim (\frac{5}{t} - \frac{5}{t ^{2} + t})

n \to \infty lim (\frac{n ^{100}}{5 0 ^{n}})

What is the solution for (d^2y)/(dx^2)y+81y=0 ?
The solution for (d^2y)/(dx^2)y+81y=0 is y=-(81x^2)/2+c_{1}x+c_{2}